Solve (i-2)*i+Jx=x/1+i

$$( i - 2 ) \cdot i + J x = \frac { x } { 1 + i }$$

Solve for J

$$J=\frac{1}{2}-\frac{1}{2}i+\frac{1+2i}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply i-2 by i.

$$-1-2i+Jx=\frac{x}{1+i}$$

Add 1+2i to both sides.

$$Jx=\frac{x}{1+i}+\left(1+2i\right)$$

The equation is in standard form.

$$xJ=\left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(1+2i\right)$$

Divide both sides by x.

$$\frac{xJ}{x}=\frac{\left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(1+2i\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$J=\frac{\left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(1+2i\right)}{x}$$

Divide \left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(1+2i\right) by x.

$$J=\frac{1}{2}-\frac{1}{2}i+\frac{1+2i}{x}$$

Solve for x

$$x=\frac{2+4i}{2J+\left(-1+i\right)}$$

$$J\neq \frac{1}{2}-\frac{1}{2}i$$